It would cost $288 to cover the larger rectangular garden.
"It is relationship between two numbers that describe how many times one value can contain another. "
"It is an equation in which two ratios are equal."
[tex]A=l\times w[/tex], where 'l' is length of the rectangle and 'w' is width of the rectangle
For given question,
Let 'l' be the length of the rectangle and the 'w' be the width of the rectangle.
The ratio of dimensions of a rectangular garden would be w:l.
mulch is needed to cover a larger, similar garden.
The ratio of dimensions is 2:3
As both the gardens are similar, their dimensions must be in proportion.
[tex]\Rightarrow \frac{w}{2}= \frac{l}{3}[/tex]
[tex]\Rightarrow \frac{w}{l}= \frac{2}{3}[/tex]
So, the length of the larger rectangular garden would be [tex]3l[/tex]
and the length of the larger rectangular garden would be 2w
A mulch to cover the first rectangular garden costs $48.
This means, for the area of [tex]A_1=l\times w[/tex] it costs $48.
Using the formula for area of rectangle the area of the larger garden would be,
[tex]A_2=3l\times 2w\\A_2=6(l\times w)\\A_2=6\times A_1[/tex]
For the second garden it would costs,
6 × 48 = 288
Therefore, it would cost $288 to cover the larger rectangular garden.
Learn more about the area of the rectangle here:
https://brainly.com/question/12019874
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